How can I do something 0.5 seconds after text changed in my EditText control?

Better use Handler with the postDelayed() method. In the Android's implementation, Timer will create a new thread each time to run the task. Handler, however, has its own Looper that can be attached to whatever thread we wish, so we won't pay an extra cost to create a thread.

Example

 Handler handler = new Handler(Looper.getMainLooper() /*UI thread*/);
 Runnable workRunnable;
 @Override public void afterTextChanged(Editable s) {
    handler.removeCallbacks(workRunnable);
    workRunnable = () -> doSmth(s.toString());
    handler.postDelayed(workRunnable, 500 /*delay*/);
 }

 private final void doSmth(String str) {
    //
 }

Use:

editText.addTextChangedListener(
    new TextWatcher() {
        @Override public void onTextChanged(CharSequence s, int start, int before, int count) { }
        @Override public void beforeTextChanged(CharSequence s, int start, int count, int after) { }

        private Timer timer = new Timer();
        private final long DELAY = 1000; // Milliseconds

        @Override
        public void afterTextChanged(final Editable s) {
            timer.cancel();
            timer = new Timer();
            timer.schedule(
                new TimerTask() {
                    @Override
                    public void run() {
                        // TODO: Do what you need here (refresh list).
                        // You will probably need to use
                        // runOnUiThread(Runnable action) for some
                        // specific actions (e.g., manipulating views).
                    }
                },
                DELAY
            );
        }
    }
);

The trick is in canceling and rescheduling Timer each time, when text in EditText gets changed.

For how long to set the delay, see this post.